Personal chronology

Iain was born on 10 July, 1949 in Edinburgh, where he grew up. He studied undergraduate mathematics at the University of Edinburgh, did Part III at Cambridge and then commenced a PhD in Aberdeen. Early in Iain’s PhD, Joe Taylor invited him to visit the University of Utah and this became a permanent move—he completed his PhD at Utah in 1976 under Joe’s supervision. He subsequently completed postdoctoral fellowships at Utah and then at Dalhousie, Canada—a hothouse for functional analysis at the time, where he met and began working with his long-time collaborator John Phillips among others.

A Newcastle department gathering (Iain second from right, second row).

In 1979, Iain moved to a permanent job at the University of New South Wales, where he worked for 12 years. He then moved to the University of Newcastle in 1990 as the Chair of Mathematics and built a truly remarkable research group in functional analysis (as Dana points out without hyperbole, there was definitely a time—say the mid 90s—when it was hard to find someone working in operator algebras who had not visited Newcastle). It was also during this golden era at Newcastle that Iain met his life partner Astrid. When times sadly turned bad at Newcastle due to university budget cuts, Iain relocated with a small group of colleagues to the University of Wollongong in 2007.

Iain and Astrid in Wellington.

In 2010, Astrid was offered a Chair at the University of Otago in Dunedin and negotiated a position there for Iain as well. They spent 7 years in Dunedin, during which time Iain was made a Fellow of the Royal Society of New Zealand, before relocating to Victoria University of Wellington in 2017. Iain retired during the COVID pandemic. He died, too young, of complications due to cancer on the 27th of September, 2023. He leaves behind his ex-wife Johann and son Fraser, his ex-partner Jane and his beloved life-partner Astrid.

Mathematical chronology

To put this chronology together, we first looked Iain up on MathSciNet. It told us that he wrote a total of 168 books and papers. Yep, one hundred and sixty-eight. In each of 1997 and 2004, it lists eight publications for Iain in the calendar year—in 2004, this included his monograph Graph $C^{\ast }$ -algebras, which remains the canonical reference for the subject. He published with 77 distinct co-authors, many of them postdocs, PhD students, and honours and undergraduate students. His work has collectively accumulated, so far, 5377 citations from 2124 distinct publications involving 1186 distinct authors. His top 10 most-cited publications alone have accumulated 2362 citations and even if you leave out his two books, that number is 1650. Iain would have been the first to point out that citation data doesn’t necessarily mean a lot, but any way you read it, those numbers tell a story of enormous influence on an enormous number of mathematicians. We would add that part of the reason for this was the enormous importance and value that Iain attached to well-written mathematics. Anyone who wrote with him has had the experience of iteration after iteration coming back covered with Iain’s inimitable red-pen scrawl. Dana, in mock frustration, once sent Iain a draft printed on red paper! Everyone in the mail room laughed out loud when Iain opened it. Iain just cheerfully went out and bought a green pen.

In any case, the volume of Iain’s work renders compiling a mathematical chronology that does justice to his impact no easy task. Our objective here is just to give an overview of the breadth of his interests, contributions and achievements. We have not included a bibliography (it would run to eight pages by itself), but you can look up Iain’s MathSciNet profile (MR143810) yourself.

We tried to categorise Iain’s work under very broad headings that each collected at least a good handful of his papers. Even so, we wound up with 14 of them and our categorisation was not as nuanced as we would like, so we have settled on discussing broad themes. One of Iain’s amazing mathematical talents was finding connections between mathematical themes and to other people’s work; so many of his papers fall under more than one heading and, in numerous cases, also incorporate ideas from elsewhere in mathematics that don’t, themselves, really fall under any of our headings at all. The point is that Iain was a broad-ranging and inclusive scholar, and that he rarely left an old mathematical interest completely behind, even as he continued to form new ones.

Iain’s PhD thesis in 1976 was concerned with the structure of the maximal-ideal space of a commutative Banach algebra and how it relates to the structure of the algebra itself. This led him into the study of perturbations of Banach algebras and then perturbations of $C^*$ -algebras, which also launched his long and fruitful collaboration with John Phillips, with whom he wrote a total of 15 papers. Aidan remembers Iain reminiscing fondly on this collaboration, which largely took place before email and involved the passing back and forth of drafts by snail mail until the author currently in charge of the manuscript was satisfied that it was done and submitted it. Iain particularly enjoyed the collaborative trust that this process represented.

Iain’s work with John led him into the broad study, starting around 1978, of Type I $C^*$ -algebras, particularly continuous-trace $C^*$ -algebras, and their automorphism groups via Čech cohomology, the Picard group and Dixmier–Douady theory, and also of cohomology and homology of $C^*$ -algebras. Iain made deep contributions to this area. One is his and John’s celebrated classification, up to unitary equivalence, of the automorphisms of a continuous-trace $C^*$ -algebra via the ‘Phillips–Raeburn obstruction’ and proof that unitary equivalence is not a smooth relation outside the continuous-trace setting. Another is the development of the ‘Raeburn–Taylor groupoid’ as a model for a continuous-trace $C^*$ -algebra with specified Dixmier–Douady invariant.

Also in 1978, Iain developed an interest in Toeplitz operators and Fredholm theory in the context of $C^*$ -algebras, which he would continue to pursue on and off over the next 20 years, particularly in collaboration with students. Iain was always on the lookout for topics that could bring good students rapidly to the coalface of live mathematical research without too much danger of them being ‘gazzumped’. A short course on Fredholm theory and the Toeplitz algebra was also one of his favourites when a cohort of good Honours students was in need of some extra material.

One of Iain’s most abiding interests was crossed products of $C^*$ -algebras by actions and coactions, Takai duality and imprimitivity theory. Starting in 1984, we count 52 papers relating to this general research theme, including some of his most prolific collaborations: with Astrid an Huef, Dana Williams, Judy Packer, John Quigg and Steve Kaliszewski. In particular, the famous ‘Packer–Raeburn Stabilisation Trick’ came out of his work in this area. Aidan remembers Iain once laughingly observing that he had a ‘Groupoid’, a ‘Trick’ and an ‘Obstruction’ but no ‘Theorem’; Aidan also thinks that the ‘Gauge-Invariant Uniqueness Theorem’ should be called the ‘an Huef–Raeburn Uniqueness Theorem’, and would have been had the authors not themselves coined a more descriptive and euphoniousFootnote ¹ alternative. Iain’s work on crossed products also led to his powerful approach to $C^*$ -algebras via universal properties; a tool by now so standard that it takes an effort to see how influential Iain was in its development and adoption.

Iain’s widely read and used 1998 book Morita equivalence and continuous-trace $C^{\ast }$ -algebras with Dana (one of 24 joint publications) came out of the intersection of this and his work on Type I $C^*$ -algebras. As his co-authors will attest, in memory of the many rounds of proofreading involved in its production, this book was always tagged in Iain’s LATEX code as $\backslash $ bibitem{tfb}. The ‘t’ stood for ‘the’ and the ‘b’ stood for ‘book’.

Around 1989, Iain began investigating the structure of semigroup $C^*$ -algebras. Later, prompted by the presence of George Willis, Jacqui Ramagge, Marcelo Laca and Neal Fowler at Newcastle in the mid 1990s, and particularly by George’s structure theory for totally disconnected locally compact groups, Iain extended his interest in semigroup $C^*$ -algebras and associated crossed products to include generalised crossed products coming from Cuntz–Pimsner theory and also the study of Hecke $C^*$ -algebras. Again, this was a source of many student projects, including an eight-author paper involving a team of five undergraduate project students.

The 2006 Málaga graph algebras workshop (Iain second from right, back row).

It was fondly referred to by its authors as the ‘Big Dog and Friends’ paper in reference to a Novocastrian kids’ TV program—Iain was ‘Big Dog’ and enjoyed the appellation.

The idea of describing $C^*$ -algebras by universal properties together with the eme rgence of Doplicher–Roberts algebras led to Iain’s pioneering work on Cuntz–Krieger algebras and graph $C^*$ -algebras starting around 1996. His 1997 paper with Astrid on the primitive-ideal spaces of Cuntz–Krieger algebras (one of 38 joint papers) demonstrated the power of the universal approach. It has become, without fanfare, the standard approach to ideal-structure analysis for $C^*$ -algebras described by universal properties. Over the next 30-ish years, Iain wrote some 30 papers relating to graph $C^*$ -algebras and their analogues, launching many research careers (including Aidan’s and Nathan’s) along the way. It is fair to say that all of the fundamental structure theory of graph $C^*$ -algebras originated with Iain.

Around 1999, Iain’s interest in semigroup $C^*$ -algebras segued into what became an enduring interest in connections between $C^*$ -algebras and number theory, particularly via Kubo–Martin–Schwinger (KMS) states. What Aidan would call the ‘Laca–Raeburn Program’ for determining the KMS states on a $C^*$ -algebra admitting a suitable Toeplitz extension, developed in Iain and Marcelo’s 2010 paper, is another instance of one of Iain’s deeply influential ideas that has subsequently quietly permeated the entire literature. It has become the standard approach to the subject and underpins tens of subsequent papers by numerous authors.

Iain was always very conscious of the need to generate research funding to maintain a healthy and vibrant research department, and he was amazingly prolific in securing funding from the Australian Research Council. Folks in Australia don’t realise, these days, that before Iain met Gavin Brown at UNSW, the general consensus was that ‘mathematicians don’t get external grants’. The health of mathematics in Australia, buoyed by ARC funding, owes a great deal to Iain’s normalising of the practice of just knuckling down and applying for it. In particular, around 2003, Iain was part of a successful bid for a big ARC Centre of Excellence in collaboration with Newcastle’s excellent Electrical Engineering department. As part of his involvement in this Centre, Iain developed an interest in wavelet bases and multiresolution analyses that he continued for many years afterwards.

Iain’s approach to developing any idea like this was to explore and refine it through applications to new classes of examples. In the instance of KMS theory, this led in 2014 to his interest in $C^*$ -algebras of self-similar groups and his subsequent development of self-similar groupoids, on which he wrote a number of substantial papers in the final years of his career.

Iain lecturing at a CIMPA school—he loved inviting young people to mathematics.

Okay, so we fail. There’s no way to capture in a few pages the depth and breadth of Iain’s impact. A list of names (ordered by number of joint publications) maybe does better: Astrid an Huef, Marcelo Laca, Steve Kaliszewski, David Pask, Aidan Sims, Nadia Larsen, Nathan Brownlowe, Alex Kumjian, Sriwulan Adji, Neal Fowler, Jacqui Ramagge, Wojciech Szymanski, Trent Yeend, Teresa Bates, Sooran Kang, Ilija Tolich, Sean Vitadello, Natasha Weaver, Michael Whittaker, James Fletcher, James Foster, Rachel Hancock, Robbie Hazlewood, Jacqueline Hicks, Helen Lindsay, Janny Lindiarni, Damian Marelli, May Nilsen, Rizky Rosjanuardi, Shaun Thompson, Sam Webster. This is a probably incomplete list of young people who got their first taste of the joys of friendly, collaborative mathematical research under Iain’s guidance and mentorship—his influence can be seen not just in his own achievements, but all that these people have gone on to achieve.

Some tributes

When it came time to write this ‘mathematical obituary’, we decided that the only way to really convey the immense impact, both mathematical and personal, that Iain had on those around him would be to ask them to give their own impressions. Here is some of what his colleagues had to say.

Nathan Brownlowe. I first met Iain in his office at the University of Newcastle in 1998. I had only been a student for a few weeks and was looking to join his real analysis class. After an encouraging conversation, I found someone’s notes, joined the class and, before long, had to hand in my first assignment. As I was coming to grips with the main ideas of a subject that felt very different to high school mathematics, Iain called me back into his office to talk about my assignment. Turns out I had absolutely no idea what an implication arrow was. A left arrow, right arrow, double arrows? Apparently, they all mean different things! I wasn’t in high school any more and I had an embarrassing lesson in how the writing of mathematical arguments is just as important as the arguments themselves. I would have this lesson from Iain almost every time I was in his office.

After I survived real analysis, Iain would go on to teach me almost everything I know about functional analysis and operator algebras. He supervised my honours year, PhD and my first stint as a postdoc. It’s fair to say that Iain completely shaped how I learned, thought about, talked about, wrote and researched mathematics. He was an amazing researcher and colleague, and I would not be where I am now without his patience and mentorship. Iain also shaped how I teach mathematics, the pinnacle of which I still consider to be Iain constructing arguments with chalk on a blackboard. I try to do him justice every time I am now in front of a class using those implication arrows.

Paul Muhly. Although I was aware of Iain’s early work and knew that he was one of my ‘mathematical cousins’, I did not meet him until the Kingston conference in the summer of 1980. And even then, our interaction was only at the social level. So, I was both surprised and flattered to receive an invitation in the Fall of 1992 to visit him in Newcastle for a month-long research visit in 1993. That visit started what turned into a steady stream of visits and interactions.

I was not the only one to visit Iain. Under Iain’s leadership, Newcastle became a mathematical Mecca. It had a magical atmosphere that encouraged mathematics and its research. It did not matter if you were working with Iain. Whatever one was working on was supported and celebrated. It was, indeed, a very special place.

While we only published one joint paper (with Neal Fowler), our discussions then and subsequently had an enormous influence on both my research and teaching.

By any measure, Iain’s efforts to stimulate his students and postdocs were amazingly successful and prescient. His contributions to mathematics and its culture are sadly missed.

Judy Packer. It was a stroke of good fortune for me to meet Iain in 1986—he was the first mathematician I felt completely comfortable talking to about mathematics. I could even talk to him about the anxiety I had experienced in doing mathematics on my own, and he told me how much more enjoyable it would be, then, to collaborate with others. Thus began my very first collaboration with another mathematician.

He was such a great mentor, champion and friend, and tremendously generous and brilliant. I think it was Dana Williams who said that Iain could write out mathematics almost like a smooth, well-oiled machine, coming out with numerous insights on parallel projects at once. 1986 was pre-e-mail and pre-TeX for me at least, so he would send his ideas for articles in his neat handwriting in manuscript form in the $8" \times 11"$ manila envelopes from UNSW. I still have some of these in my files.

His impact on my professional career was incalculable, and he was a great and kind mentor to me and many others, and so modest despite his numerous contributions to our field. I will miss him terribly.

David Pask. My life is better for having known Iain Raeburn. He took me on as a postdoc and helped me at several vital stages of my career. Apart from being a great mathematician and leader, he created a rich, happy environment in the School of Mathematics at the University of Newcastle. He loved socialising with his circle of friends and visitors to the School. His high publication rate at this time reflected his creativity and many grant successes.

Rae Pease. I had the honour of working in the office of the Department of Mathematics at the University of Newcastle when Iain took up the position of Professor of Mathematics. We had adjoining offices, and quickly developed a strong working relationship and enduring friendship. I will be forever grateful for his mentorship and support in helping me develop my career. The efforts he made—often in his own time and through numerous restructures—to ensure I was correctly classified and eventually promoted to School Executive Officer were phenomenal.

In establishing his research group at Newcastle, Iain not only invigorated the department mathematically, but also fostered a unique, multicultural and vibrant friendship group through the influx of new staff and a steady stream of research visitors. He understood that attracting visitors to Newcastle, away from the capital cities, meant ensuring they had an enjoyable experience. The resulting collaborations—joint research papers, grant applications and books—stand as testament to the success of this approach. My family was fortunate to be included in many of the dinners, vineyard excursions and bushwalking trips to the Blue Mountains, all accompanied by lively mathematical conversation. We remain friends with many of those visitors to this day.

Iain’s generosity of spirit in encouraging the research of all academics in the department was unmistakable. While he was responsible for departmental funds, conference registration, travel and basic accommodation were made available to all. This was a clear priority for him in building a research-intensive department.

In a similar vein, I recall a visit from one of my son’s engineering friends, who came to me lamenting a difficult mathematics problem. Iain happened to be walking past on his way to his office when I called him over. In just a few seconds, he offered a clear and concise explanation. As the student left, he turned to me and said, ‘This guy’s good’. So true—and perhaps the understatement of the century.

John Quigg. Iain Raeburn was a brilliant mathematician and a truly generous collaborator. I had the privilege of working with him for over two decades, visiting him in Australia and New Zealand nearly every year from 1991 to 2014, resulting in ten co-authored papers. Many times, while working together in his office, we would reach a difficult point in our research. Iain would simply stare out the window for thirty seconds and then, as if by magic, the solution would appear in his head, fully formed. This remarkable ability was just one aspect of his sharpness as a $C^*$ -algebraist, and he was always unfailingly generous with his time and insights.

Beyond our mathematical collaboration, Iain and I developed a strong personal friendship. We shared a mutual love for the outdoors and some of my fondest memories with him are from the many hikes we took together. We were also avid beer enthusiasts and our shared enjoyment of a good brew often punctuated our days, adding to the camaraderie that made our time together so special. His keen intellect, kind spirit and wonderful sense of humour made him an exceptional colleague and a great friend.

Aidan Sims. Iain was my great mentor and friend. I first met him at departmental parties at my dad’s place in Newcastle. He later taught me numerous undergraduate courses (some of which he cheerfully created on top of his other teaching duties just to keep enthusiastic young folk occupied); he supervised my honours and then my PhD; he generated the funding that led to my first postdoc; and he made a personal sacrifice in moving to Wollongong (there is no doubt that UNSW, where Astrid was working at the time, would have leapt if he’d asked) to secure a permanent position there for me.

Even when I was an undergraduate, honours and then PhD student, Iain was as much friend as professor and advisor. He always welcomed the whole departmental community—students, professional staff, visitors and academics from every walk of mathematics—to social events like the famous Wednesday afternoon social tennis games, and the Thursday afternoon seminars and post-seminar drinks and dinners: Iain wove the simple magic of unreserved welcome that made Newcastle what it was. So, over the years, we became close friends as well as long-time collaborators. If I manage to do or write mathematics even half as beautifully as Iain did, it’s twice as well as I’d have managed without his guidance, encouragement and red pen. After Astrid and Iain moved to New Zealand, I took every possible opportunity to visit, to learn more mathematics and to learn about Kiwi flora on the many hikes, or ‘rambles’, that were Iain’s joy. I feel immensely lucky to have had such a wonderful ‘mathematical father’.

Dana Williams. Iain and I first met almost half a century ago. We remained close friends and collaborators until his passing. We shared many adventures—both mathematical and personal—which have shaped my career and my life. We spent many hours strolling the streets and bush of Australia, often discussing things ranging from the nuances of our current research project to the distinction between rugby league and rugby union. Iain never opted for a mundane approach. We often walked from the office to his home for dinner and I marvelled at how complex the route was until I had to find my own way one weekend. I only then realised he never took the same route twice and that there was a nice direct, but boring, route. As usual, there was something to learn from him here. His approach to mathematics was just as bold and equally edifying.

Like everyone else who worked with Iain, I learned a lot of mathematics. However, I learned a good deal more than that. I learned how important it was to nurture young mathematicians and to ‘pay it forward’ by making sure our junior colleagues got the same opportunities we had enjoyed in our early careers. I learned the value of working hard to ensure that your own department was a welcoming and friendly place for colleagues and students.

Iain leaves an immense legacy in his wake. His generosity ranged from the odd honours student who got one great opportunity to see real mathematics close up, to those PhD students and other young colleagues who were given the opportunity and guidance to start stellar careers of their own.

Significantly, Iain’s energy, vitality and good nature energised his surroundings. Whatever institution he called home became a centre of mathematical activity. Visitors came from all over to experience the intellectual atmosphere and the social ambiance. I can’t begin to enumerate all the productive and enjoyable visits I made to work with Iain over the years. I will always treasure those memories.